Transcript Patterns and Inductive Reasoning

Patterns and Inductive
Reasoning
During this lesson, you will
use inductive reasoning to make
conjectures.
Mrs. McConaughy
Geometry
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Standards/Assessment Anchors:
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Geometry
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Daily Warm Up
Inductive reasoning ___________
Conjecture
__________________________
Give an example of when you have
used inductive reasoning in the
real world.
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Vocabulary
Inductive reasoning reasoning
________________
based upon
______________________________
patterns
you observe.
the conclusion you reach
Conjecture ______________________
using
inductive reasoning
_______________________________
an example for which the
Counterexample ___________________
conjecture is incorrect
_______________________________
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Finding and Using a Pattern
Examples: Number and
Letter Patterns
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Finding and Using a Pattern
Use inductive reasoning to a. find a pattern
for each sequence, then b. use the pattern to
find the next term in each sequence below:
20, 18, 16, 14, 12
__
U
A, C, F, J, O, __
1, 3, 6, 10, 15, 21, ___
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a, 6, c, 12, e, 18, __
g
½, 9, 2/3, 10, ¾, 11, 4/5
__
1, 3/2, 9/4, 27/8, 81/16
__
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Using Inductive Reasoning to Make
Conjectures
EXAMPLE
EXAMPLE
3+5=8
-3 + 5 = 2
-1 + 1 = 0
13 +27 = 40
51 + 85 = 136
Conjecture: The sum of
two odd numbers is
even integer
always an
___________.
3 * 4 = 12
12 * 5 = 60
11 * -4 = -44
-24 * -3 = 72
-7 * 8 = - 56
Conjecture: The product
a prime number and
of ______________
an_________________
even integer is always
an_________________.
even integer.
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Finding and Using a Pattern
Examples: Picture Patterns
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EXAMPLE: Testing a Conjecture
When points on a circle are joined by as many
segments as possible, overlapping regions are formed
inside the circle as shown above. Use inductive
reasoning to make a conjecture about the number
of regions formed when five points are connected.
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Did
you aguess
that thetonumber
Now find
counterexample
show thisof
conjecture
false. at each stage?
regions is
doubles
Points
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Regions
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2
3
4
4
8
5
16
6
?
31
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Testing a Conjecture
Not all conjectures turn out to
be true. You can prove that a
conjecture is false by finding
one counterexample.
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Applying Conjectures to Business
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Final Checks for Understanding
1. Find the next term in the following
sequence:
2. Use inductive reasoning to make a
conjecture:
3. Counterexample:
4. Draw the next picture in the picture
pattern below:
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Geometry
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Homework Assignments:
Day 1: Inductive Reasoning WS
Day 2: Number Patterns WS
Day 3: Picture Patterns WS
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